Merriam-Webster's Word of the Day for November 21, 2008 is:

non sequitur • \NAHN-SEK-wuh-ter\  • noun
1 : an inference that does not follow from the premises *2 : a statement (as a response) that does not follow logically from or is not clearly related to anything previously said

Example sentence:
The professor's lecture was a jumble of non sequiturs and irrelevant observations.

Did you know?
In Latin, "non sequitur" means "it does not follow." The phrase was borrowed into English in the 1500s by people who made a formal study of logic. For them it meant a conclusion that does not follow from the statements that lead to it. But we now use "non sequitur" for any kind of statement that seems to come out of the blue. The Latin verb "sequi" ("to follow") has actually led the way for a number of English words. A "sequel" follows the original novel, film, or television show. Someone "obsequious" follows another about, flattering and fawning. And an action is often followed by its "consequence."

*Indicates the sense illustrated in the example sentence.